Ask Dr. Faizal 1 – The Classical and Quantum Understandings of the World

By Dr. Mir Faizal and Scott Douglas Jacobsen

Dr. Mir Faizal is an Adjunct Professor in Physics and Astronomy at the University of Lethbridge and a Visiting Professor in Irving K. Barber School of Arts and Sciences at the University of British Columbia – Okanagan.

Here we start the cosmology educational series on the differences between the classical and the quantum worlds.

Scott Douglas Jacobsen: We have heard terms like classical physics and quantum physics. What do these terms mean in simple words, and what is the difference between them?

Dr. Mir Faizal: We have evolved at a certain scale, and our intuitive understanding of the world is also limited to that scale. Now common sense is the expression of this intuitive understanding of the world in languages like English or French. If this intuitive understanding of the world is expressed in mathematics, we naturally will obtain a mathematical description of common sense. This mathematical description of our intuitive understanding is called classical physics. However, there is no fundamental reason why such a description will hold at a different scale. In fact, now we have known that the classical description does not hold at very small scales, and common sense seems also to break at such a scale. It is hard to accurately describe the world at such a small scale using languages like English or French, as these languages have not been evolved to describe the world at such a scale. However, it is still possible to mathematically describe the world at such a small scale, and this mathematical description of a small scale is called quantum physics. Even though it is not possible to describe the world at such a small scale in common language, it is possible to use analogies to understand physics at such small scales.

Jacobsen: We see the world around us, and know how it behaves, and this forms a basis for our common sense. You mentioned that our common sense breaks in quantum mechanical. Can you give some examples of such a breaking of common sense in quantum mechanics? 

Faizal: Let us start by a simple example, to understand how the common sense breaks in the quantum mechanism. If there are two paths between your home and your office, and you are travelling between them, you can take any one of these two path at one time. However, you will infer that it is impossible to take both these paths at the same time. Even if you are really tiny, you cannot take two paths at the same time. The main reason for this is that it is impossible for you to be present at two different places at the same time. This seems to be something that you know from common sense. However, this description of the world does not hold at much smaller scales. In quantum mechanics, you go to your office from both those paths. In fact, you will take all the possible paths between your home and office, and we have to mathematically sum these path to describe your behaviour of going between your home and office. This is actually how things are calculated for quantum mechanical particles. This description of quantum mechanics (where a particle takes all possible path between two points) is called the Feynman path integral approach.

Jacobsen: We have seen people commute between their home and office. In fact, as more simple system, we have seen a stone fall down, and it does not appear to take many paths between two points. We have also never seen a particle present at two places at the same time. How does the quantum mechanical fit with these observations? 

Faizal: In quantum mechanics, as soon as someone makes a measurement on some object, it instantaneously collapses to just one of those paths. Now it is possible to calculate the chance of an object to be collapse to a certain path in quantum mechanics. For large enough objects, this almost coincides with the path that the object is expected to take based on classical mechanics. However, as the objects gets smaller, the deviations between the two paths becomes significant. It may be noted to calculate the position of an object at any point in future, you need to know about two things. You need to know where that object is present at a given time, and you need to know how fast it is travelling in a certain direction. If you know both these things, then you can know where that object will be present in future. However, in quantum mechanics, it is impossible to measure both the position of a particle and how fast it is travelling, at the same time. Thus, in quantum mechanics it is not possible to accurately measure the position of a particle in future. What we can measure is the chance for a particle to be present at a certain point in time. So, in quantum mechanics causality is also only probabilistically true. As it is impossible to obtain certain knowledge of cause, the effects can be only probabilistically predicted. 

Jacobsen: It is possible to exactly predict the future position of a particle by improving our technology and inventing better devices?

Faizal: Technological development cannot be used to predict the future position of a particle beyond what is allowed by quantum mechanics. This is because for such quantum system certain knowledge is actually not present in nature, and so we can only get probabilistic knowledge of such system. This is the main difference between the classical and quantum description of the world. In classical mechanics, at least in principle, it is possible to know the behaviour of a particle with certainty. In other world, the world is totally deterministic in classical mechanics. It might be difficult to exactly calculate such a behaviour, but such a knowledge exists in nature. In fact, even in classical mechanics, we usually use probability to describe the world. This is the basis of statistical mechanics. However, such a use of probability is epistemological as certain knowledge exists at an ontological level in classical physics. It is just very difficult for us to obtain such knowledge accurately for many systems. However, in quantum mechanics there is an ontological use probability as certain knowledge is absent at an ontological level from nature.

Jacobsen: Can you give a simple analogy of this difference to make it easy to understand? 

Faizal: Let us again use a simple example to understand this difference. Someone is going to a coffee shop, and he usually likes to drink coffee but sometime orders tea. As it is a coffee shop they keep running out of tea. Now if it is known that he takes tea about twenty times in hundred days, then you can calculate the chance of him drinking tea of coffee. You cannot predict accurately what he will take on a given day, as such a knowledge is not present in this system. However, knowing what he is more likely to order, you can predict his behaviour over a large number of visits. So, for the next ten days you can save two tea bag for him. This is an example of an ontological absence of knowledge, and this is how probabilities work in quantum mechanics. Now consider another example, in a group of ten people, two of them like tea and the rest like coffee. Also they have a rule that they will not visit the coffee shop more than once in ten days. Now if you do not bother to ask them who like tea and who likes coffee, and just know how they behave in a group, you can again predict the probability of them drinking tea. However, in this case, the knowledge exists in form a hidden variable, which you did not bother to measure. This is an example of an epistemological absence of knowledge, and this is how probabilities work in statistical mechanics.

Jacobsen: I can understand that certain knowledge of the particle is not present, but where is the particle actually present. 

Faizal: The particle is present at every possible point it can occupy, till it is measured. However, when it is measured, it instantaneously collapses to a single point, and we can measure the chance of it collapsing to a certain point. This is an important feature of quantum mechanics. In classical mechanics, two different contradictions cannot be simultaneously existing. In quantum mechanics, all possibilities simultaneously exist, till they are measured. However, when they are measured, only one of them is instantaneously observed, and the system ceases to exist in the other possibilities. This principle has been illustrated by the famous thought experiment of Schrodinger’s cat, in which a cat is killed by a quantum mechanical process. There are two possibilities, as the cat can be dead and alive. Now if the system is not observed, then the cat can exist in a state being dead and alive at the same time. As soon as an observation is made, the system instantaneously collapses to one of the two possibilities, so the cat is actually observed to be dead or alive. However, if no observation is made, the cat is in a state of being dead and alive at the same time. 

Jacobsen: Can these quantum effects be observed in our daily life?

Faizal: A important requirement of quantum mechanics is that it should coincide with the classical physics at our scale, for all the system that have been described using classical mechanics. This means these quantum effects become so small at our scale that they can be neglected, and cannot be observed. There are few phenomena like superconductivity and superfluidity where quantum effects can change the behaviour of certain system at large scale. However, most quantum mechanical effect, which break common sense, can be neglected at our scale, and the world at our scale can described by classical mechanics. It is possible that there are some systems, where other quantum effects become important even at large scale, and their behaviour is very different from the behaviour predicted from classical mechanics. 

Jacobsen: Thank you for the opportunity and your time, Dr. Faizal.Faizal: My pleasure. 

Photo by Billy Huynh on Unsplash